Asian Journal of Mathematics and Computer Research

Stability Analysis of Modified General Version of Gauss-type Proximal Point Method for Solving Generalized Equations Using Metrically Regular Mapping

Asian Journal of Mathematics and Computer Research, Volume 30, Issue 2, Page 38-52
DOI: 10.56557/ajomcor/2023/v30i28294

Abstract


A modified general version of Gauss-type proximal point algorithm (GGPPA) is presented in this article for solving the parameterized generalized equation y ∈ F(x), where y is a parameter and a set-valued mapping F: X ⇉ 2Y is acting between two different Banach spaces X and Y. We demonstrate the existence of any sequence produced by the modified GGPPA by taking certain presumptions into account, and we use metrically regular mapping to demonstrate the uniformity of semi-local and local convergence findings. Finally, we present a numerical experiment to verify the uniformity of semi-local convergence result.

Keywords:
  • Set-valued mapping
  • metrically regular mapping
  • semi-local convergence
  • uniform convergence
  • lipschitz continuity
  • fixed point lemma

How to Cite

Alom , M. A., & Rahman , M. Z. (2023). Stability Analysis of Modified General Version of Gauss-type Proximal Point Method for Solving Generalized Equations Using Metrically Regular Mapping. Asian Journal of Mathematics and Computer Research, 30(2), 38–52. https://doi.org/10.56557/ajomcor/2023/v30i28294

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